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the back for a 13 is about 54 inches long. You should measure yours, you want it to fit inside the side rails. To support it, whaler used boomerang's You can see them if you download the plans for the Eastport Stern Seat. For the 13, the flat sides of the boomerang are 11 inches long. Just like the ones on the eastport there is 1 3/8 inches from where the straight seat part of the seat to where the straight part for the seat back would come down. Remember that the back is not 90 degrees to the seat, it's tilted slightly back.
before you make the boomerang out of mahogany, i would suggest you try a couple out of plywood to get the angles right. To attach them to the seat make some some mahogany blocks. The blocks are screwed to the underside of the seat and the back, then the boomerang is screwed into the blocks.